|
278 | 278 | #+end_src
|
279 | 279 |
|
280 | 280 |
|
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| -** Introduction to the t distribution :ignore: |
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| - |
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| -#+RESULTS: sampling4 |
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| -[[file:bsample4.png]] |
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| - |
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| -#+NAME: sampling4 |
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| -#+BEGIN_SRC R :results output graphics :exports results :file bsample4.png :width 2500 :height 2000 :res 300 |
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| - library(data.table) |
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| - library(ggplot2) |
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| - options(scipen=9999) |
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| - readRDS("plfsdata/plfsacjdata.rds")->worker |
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| - worker$standardwage->worker$wage |
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| - c(1:nrow(worker))->worker$SamplingFrameOrder |
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| - worker[sex!=3,]->worker |
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| - |
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| - worker->t9 |
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| - (t9$wage-mean(t9$wage))/sqrt(var(t9$wage))->t9$wage |
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| - ggplot(t9,aes(wage))+geom_density(colour="black",size=1)->p |
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| - p+scale_y_continuous(limits=c(0,0.75))->p |
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| - p+scale_x_continuous(limits=c(-15,15) |
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| - ,breaks=c(-15,0,round(mean(worker$wage)),15))->p |
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| - p+theme_bw()->p |
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| - p |
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| - |
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| - data.frame(sno=c(),meancol=c(),sterr=c())->t4 |
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| - samplesize=50 |
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| - for (i in c(1:20000)) { |
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| - sample(1:nrow(worker),samplesize, replace=FALSE)->a1 |
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| - worker[a1,]->s1 |
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| - rbind(t4,data.frame( |
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| - sno=i, |
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| - meancol=mean(s1$wage), |
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| - sterr=sqrt(var(s1$wage))/sqrt(samplesize)))->t4 |
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| - } |
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| - |
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| - (t4$meancol-mean(t4$meancol))/t4$sterr->t4$teststat |
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| - (t4$meancol-mean(t4$meancol))/sqrt(var(t4$meancol))->t4$teststat2 |
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| - data.frame(modelt=rt(20000,29))->m |
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| - |
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| - var(t4$teststat) |
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| - var(m$modelt) |
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| - var(t4$teststat2) |
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| - |
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| - ggplot()->p |
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| - p+geom_density(data=t4,aes(teststat),colour="blue",size=1)-> p |
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| - p+geom_density(data=m,aes(modelt),colour="darkolivegreen",size=1)->p |
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| - p+geom_density(data=t4,aes(teststat2),colour="red",size=1)-> p |
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| - p+annotate("text",x=3,y=0.4, |
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| - label=paste("Var of statistic with unknown variance:", |
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| - round(var(t4$teststat),2)), |
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| - colour="blue")->p |
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| - p+annotate("text",x=3,y=0.39, |
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| - label=paste("Var of statistic with known variance:", |
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| - round(var(t4$teststat2),2)), |
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| - colour="red")->p |
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| - p+annotate("text",x=3,y=0.38, |
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| - label=paste("Var of t-distribution:",round(var(m$modelt),2)), |
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| - colour="darkolivegreen")->p |
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| - p |
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| - |
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| - |
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| -#+end_src |
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| - |
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| - |
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| - |
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| - |
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